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25 February, 19:07

Factor completely. 6x^4-9x^3-36x^2+54x

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Answers (2)
  1. 25 February, 19:36
    0
    3x (2x - 3) (x^2 - 6)

    Step-by-step explanation:

    6x^4 - 9x^3 - 36x^2 + 54x =

    First, factor out the largest common factor of all terms. It is 3x.

    = 3x (2x^3 - 3x^2 - 12x + 18)

    Now you have 4 terms inside the parentheses. Try factoring by grouping. Factor a the largest common factor out of the first two terms, and factor the largest common factor out of the last two terms.

    = 3x[x^2 (2x - 3) - 6 (2x - 3) ]

    Now you have a common term of (2x - 3), so factor that out.

    = 3x (2x - 3) (x^2 - 6)

    Factoring means factoring completely, so we look at each factor to see if it can be factored further. Let's look at each factor.

    3x is not factorable.

    2x - 3 is not factorable.

    x^2 - 6 is a difference, but since 6 is not a perfect square, it is not a difference of squares, so it cannot be factored.

    Answer: 3x (2x - 3) (x^2 - 6)
  2. 25 February, 20:41
    0
    3x (2x-3) (x2-6)
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